The end structure of a graph: Recent results and open problems
type: Item
instance of: scholarly article
title: The end structure of a graph: Recent results and open problems
zbMATH Open document ID: 0780.05012
DOI: 10.1016/0012-365X(92)90650-5
published in: Discrete Mathematics
publication date: 1993-01-16T00:00:00Z
review text: This is a well-written survey about the recent development in the area of ends of infinite graphs. The author introduces the reader to the topic starting with the founding results and problems of Halin (1964), mentioning previous independent but related group-theoretical investigations of Hopf (1943) and Freudenthal (1944). The five sections: 1. Introduction. 2. End-faithful spanning trees, 3. One-ended graphs, 4. Endings and tree-decompositions, and 5. Topological aspects, present leading questions, important results (some provided with a proof), desription of methods and comments of an expert in the field. Reading of this paper will be useful to anyone interested to know more about this interesting part of the theory of infinite graphs.
Mathematics Subject Classification ID: 05C05
zbMATH DE Number: 90267
zbMATH Keywords: end
zbMATH Keywords: open problems
zbMATH Keywords: survey
zbMATH Keywords: infinite graphs
zbMATH Keywords: spanning trees
zbMATH Keywords: tree- decompositions
author: Reinhard Diestel
reviewed by: Martin Škoviera
MaRDI profile type: Publication
cites work: Q3994461
cites work: Q3999150
cites work: On end-faithful spanning trees in infinite graphs
cites work: On spanning trees and \(k\)-connectedness in infinite graphs
cites work: A proof of the bounded graph conjecture
cites work: Über die Enden diskreter Räume und Gruppen
cites work: Über unendliche Wege in Graphen
cites work: Q4117857
cites work: Q3929755
cites work: A survey on graphs with polynomial growth
cites work: Wurzelbäume und unendliche Wege in Graphen
cites work: Q3484856
cites work: An end-faithful spanning tree counterexample
cites work: End-faithful forests and spanning trees in infinite graphs
cites work: Infinite connected graphs with no end-preserving spanning trees
cites work: Vertex-transitive graphs and accessibility
description: scientific article; zbMATH DE number 90267